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 Fibonacci

 http://functions.wolfram.com/04.11.16.0032.01

 Input Form

 Fibonacci[n]^3 == (1/5) (3 (-1)^(1 + n) Fibonacci[n] + Fibonacci[3 n]) /; Element[n, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Fibonacci", "[", "n", "]"]], "3"], "\[Equal]", RowBox[List[FractionBox["1", "5"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "+", "n"]]], " ", RowBox[List["Fibonacci", "[", "n", "]"]]]], "+", RowBox[List["Fibonacci", "[", RowBox[List["3", " ", "n"]], "]"]]]], ")"]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

 MathML Form

 F TagBox["F", Fibonacci] n 3 1 5 ( 3 ( - 1 ) n + 1 F TagBox["F", Fibonacci] n + F TagBox["F", Fibonacci] 3 n ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] Condition Fibonacci n 3 1 5 3 -1 n 1 Fibonacci n Fibonacci 3 n n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["Fibonacci", "[", "n_", "]"]], "3"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "5"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "+", "n"]]], " ", RowBox[List["Fibonacci", "[", "n", "]"]]]], "+", RowBox[List["Fibonacci", "[", RowBox[List["3", " ", "n"]], "]"]]]], ")"]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02